The present invention relates to optimization of complex systems under uncertainty, and more specifically, to data-driven distributionally robust optimization of complex systems.
Many of today's complex systems require decision making that is affected by uncertainty in one or more system parameters, such as usage or demand. Currently, data relating to the uncertain aspects of these systems is periodically collected by one or more sensors or meters. Current robust optimization models only exploit the collected usage data for support information of distributions for the uncertain parameters, which often leads to overly conservative models. Current distributionally robust optimization systems only exploit the observed data to construct distributional uncertainty sets consistent with the first two moments of the observed data and/or handle only restrictive classes of objective functions and constraints. On the other hand, current stochastic optimization models require highly accurate knowledge of distribution of uncertain system parameters.
Furthermore, in large-scale systems characterization of uncertainty of system parameters given based on collected data can be challenging.
Optimization models of complex real-world systems often involve nonlinear functionalities in objective and constraints. However, current distributionally robust optimization models can not take into account broad classes of nonlinearities in objective and constraints.